Final answer:
To find the equation for the function passing through two points, we calculate the slope and y-intercept using the given formula and substitute the values into the slope-intercept form. The equation is y = (1/2)x + 10.
Step-by-step explanation:
To find the equation for the function passing through the points (2, 11) and (8, 14), we need to determine the slope and the y-intercept.
First, let's find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the coordinates, we get: m = (14 - 11) / (8 - 2) = 3 / 6 = 1/2.
Next, we can use the slope-intercept form (y = mx + b) and substitute any of the given points to solve for the y-intercept (b). Taking (2, 11) as an example, we have: 11 = (1/2)*2 + b. Solving for b, we get b = 10.
Therefore, the equation to represent this function is y = (1/2)x + 10.